Algebra worksheet — GCSE Foundation

1.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

2.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

3.Solve the inequality 2(x − 1) ≤ 8.

4.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

5.Work out the value of 3n − 2 when n = 1

6.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

7.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

8.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

9.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

10.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

11.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

12.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

13.Solve 3(2x − 1) = 27

14.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

15.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.